Apparatus and method for imaging a subsurface using accumulated energy of wavefield

ABSTRACT

Provided is an apparatus of imaging a subsurface of a target area. The apparatus includes: an observed wavefield acquiring unit configured to acquire an observed wavefield for a target area based on seismic data; a parameter storage configured to store a characteristic parameter for the target area; a modeled wavefield creator configured to create a modeled wavefield corresponding to the observed wavefield using the characteristic parameter stored in the parameter storage; an energy calculator configured to calculate accumulated energies of the observed wavefield and the modeled wavefield, wherein the accumulated energies are defined as energies accumulated over time with respect to the observed wavefield and the modeled wavefield; and a parameter updating unit configured to update the characteristic parameter stored in the parameter storage such that a difference between the accumulated energy of the observed wavefield and the accumulated energy of the modeled wavefield is minimized.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims the benefit under 35 U.S.C. §119 of U.S. PatentApplication No. 61/303,258, filed on Feb. 10, 2010, and Korean PatentApplication No. 10-2010-0082162, filed on Aug. 24, 2010, the entiredisclosure of each of which is incorporated herein by reference for allpurposes.

BACKGROUND

1. Field

The following description relates to subsurface survey, and moreparticularly, to a technique for imaging a subsurface through signalprocessing using waveform inversion.

2. Description of the Related Art

Waveform inversion is a technique of estimating a velocity model of thesubsurface using prestack seismic data.

The waveform inversion means a series of processes for obtaining asubsurface structure model close to the actual subsurface structure ofan area of interest by creating an initial model for the area ofinterest, obtaining observed wavefield on the area of interest, anditeratively updating the initial model using the observed wavefield. Theprocesses are carried out by calculating modeled wavefield from anarbitrary subsurface using a computer and iteratively updatingparameters representing the physical characteristics of the subsurfacesuch that the differences of the theoretical values and data obtainedthrough actual field exploration are minimized.

Waveform inversion is one method of analyzing the subsurface structureof an area, which is one of the goals of geophysical exploration, andvarious mathematical methods are suggested. One of representativemathematical methods for waveform inversion is an ‘iterativeleast-squares method’. Generally, a unique solution does not exist inwaveform inversion. Thus, a method of obtaining an optimal solution byadding a particular condition is used in waveform inversion. In thiscase, it is optional whether to give weight to convergence or to obtaina more accurate solution from a given measured data. Since an inversemodel must be simplified and often requires extreme assumptions, it isimportant in waveform inversion to make the most of prior geologicalinformation related to geophysical characteristics.

One of the most important geological and physical characteristics foraccurate subsurface imaging is the seismic propagation velocity of thesubsurface medium. Recently, studies into a technique of artificiallyexploding a source wavelet into a target area, measuring a seismic waveagainst the target area and performing waveform inversion in a timedomain or frequency domain on seismic data, i.e., data on a seismic wavereflected or refracted by the target area to obtain a seismicpropagation velocity with respect to the subsurface medium are activelygoing on.

SUMMARY

The following description relates to a subsurface imaging apparatus andmethod that can efficiently use insufficient low frequency components inreal data in order to obtain a velocity model close to a realsubsurface.

In one general aspect, there is provided an apparatus of imaging asubsurface of a target area, the apparatus including: an observedwavefield acquiring unit configured to acquire an observed wavefield fora target area based on seismic data, a parameter storage configured tostore a characteristic parameter for the target area, a modeledwavefield creator configured to create a modeled wavefield correspondingto the observed wavefield using the characteristic parameter stored inthe parameter storage, an energy calculator configured to calculateaccumulated energies of the observed wavefield and the modeledwavefield, the accumulated energies being defined as energiesaccumulated over time with respect to the observed wavefield and themodeled wavefield, and a parameter updating unit configured to updatethe characteristic parameter stored in the parameter storage such that adifference between the accumulated energy of the observed wavefield andthe accumulated energy of the modeled wavefield is minimized.

In the apparatus, the energy calculator may be further configured tocalculate the accumulated energies of the observed wavefield and themodeled wavefield, based on values obtained by integrating the p-thpowers of absolute values of the observed wavefield and the modeledwavefield over time.

In the apparatus, the parameter updating unit may be further configuredto: define an objective function that represents a difference betweenthe accumulated energy of the observed wavefield and the accumulatedenergy of the modeled wavefield at each time-window, and update thecharacteristic parameter using a gradient of the objective function.

In the apparatus, the parameter updating unit may be further configuredto define the objective function using the accumulated energy of theobserved wavefield and the accumulated energy of the modeled wavefield.

In the apparatus, the parameter updating unit may be further configuredto define the objective function using values obtained by taking logs ofthe accumulated energy of the observed wavefield and the accumulatedenergy of the modeled wavefield.

In the apparatus, the parameter updating unit may be further configuredto calculate the gradient of the objective function using a Jacobianwith respect to a characteristic parameter of the accumulated energy ofthe modeled wavefield.

In the apparatus, the parameter updating unit may be further configuredto calculate the Jacobian with respect to the characteristic parameterof the accumulated energy of the modeled wavefield, by numericalapproximation according to a finite differential method.

In the apparatus, the characteristic parameter may include a seismicvelocity with respect to the target area.

The apparatus may further include a velocity model creator configured tocreate a velocity model of the target area using the updatedcharacteristic parameter.

In another general aspect, there is provided a method of imaging asubsurface of a target area, the method including: acquiring an observedwavefield for a target area based on seismic data, setting acharacteristic parameter for the target area and creating a modeledwavefield corresponding to the observed wavefield using thecharacteristic parameter, calculating accumulated energies of theobserved wavefield and the modeled wavefield, wherein the accumulatedenergies are defined as energies accumulated over time with respect tothe observed wavefield and the modeled wavefield, and updating thecharacteristic parameter such that a difference between the accumulatedenergy of the observed wavefield and the accumulated energy of themodeled wavefield is minimized.

In the method, the calculating of the accumulated energies of theobserved wavefield and the modeled wavefield may include calculating theaccumulated energies of the observed wavefield and the modeledwavefield, based on values obtained by integrating the p-th powers ofabsolute values of the observed wavefield and the modeled wavefield overtime.

In the method, the updating of the characteristic parameter may include:defining an objective function that represents a difference between theaccumulated energy of the observed wavefield and the accumulated energyof the modeled wavefield at each time-window, and updating thecharacteristic function using a gradient of the objective function.

In the method, the updating of the characteristic parameter may includedefining the objective function using the accumulated energy of theobserved wavefield and the accumulated energy of the modeled wavefield.

In the method, the updating of the characteristic parameter may includedefining the objective function using values obtained by taking logs ofthe accumulated energy of the observed wavefield and the accumulatedenergy of the modeled wavefield.

In the method, the updating of the characteristic parameter may includecalculating the gradient of the objective function using a Jacobian withrespect to a characteristic parameter of the accumulated energy of themodeled wavefield.

In the method, the updating of the characteristic parameter may includecalculating the Jacobian with respect to the characteristic parameter ofthe accumulated energy of the modeled wavefield, by numericalapproximation according to a finite differential method.

In the method, the characteristic parameter may include a seismicvelocity with respect to the target area.

The method may further include a velocity model of the target area usingthe updated characteristic parameter.

Other features and aspects may be apparent from the following detaileddescription, the drawings, and the claims.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates a schematic configuration of an example of asubsurface imaging apparatus.

FIG. 2 is a view for explaining an example of a waveform inversiontheory.

FIG. 3 is a diagram illustrating an example of a subsurface imagingapparatus.

FIG. 4 is a flowchart illustrating an example of a subsurface imagingmethod.

FIG. 5 is a flowchart illustrating an example of a characteristicparameter updating method.

FIGS. 6A and 6B are graphs showing an observed wavefield and the energyof the observed wavefield.

Throughout the drawings and the detailed description, unless otherwisedescribed, the same drawing reference numerals should be understood torefer to the same elements, features, and structures. The relative sizeand depiction of these elements may be exaggerated for clarity,illustration, and convenience.

DETAILED DESCRIPTION

The following detailed description is provided to assist the reader ingaining a comprehensive understanding of the methods, apparatuses,and/or systems described herein. Accordingly, various changes,modifications, and equivalents of the systems, apparatuses and/ormethods described herein will be suggested to those of ordinary skill inthe art. The progression of processing steps and/or operations describedis an example; however, the sequence of steps and/or operations is notlimited to that set forth herein and may be changed as is known in theart, with the exception of steps and/or operations necessarily occurringin a certain order. Also, descriptions of well-known functions andconstructions may be omitted for increased clarity and conciseness.

FIG. 1 illustrates a schematic configuration of an example of asubsurface imaging apparatus.

Referring to FIG. 1, the subsurface imaging apparatus may include asource 102 provided on a target area 101, a plurality of receivers 103,and a signal processor 104. The source 102 generates a sound wave and anoscillating wave. The sound wave and oscillating wave are transferred tothe target area 101. The receivers 103 measure the reflected waves ofthe sound wave and oscillating wave against several points of the targetarea 101. The characteristics of the sound wave or oscillating wavemeasured by each receiver 103 depend on the subsurface of the targetarea 101. The signal processor 104 processes the reflected sound wave oroscillating waves, thus generating image data for the target area 101.

In order to generate image data for the target area 101, the signalprocessor 104 may create a velocity model for the target area 101. Thevelocity model may represent a velocity distribution of the target area101 obtained by applying a seismic wave to the target area 101. Forexample, since the velocity of a seismic wave applied to the target area101 depends on the characteristics (for example, the kinds or densitiesof mediums) of the inner parts of the target area 101, the subsurface ofthe target area 101 may be easily imaged by obtaining a velocity modelthat represents the velocity distribution of the seismic wave.

Also, the signal processor 104 may create the velocity model throughwaveform inversion. The waveform inversion means a series of processesfor obtaining a subsurface structure model close to the actualsubsurface structure of an area of interest by creating an initial modelfor the area of interest, obtaining measurement values on the area ofinterest, and iteratively updating the initial model using themeasurement values. For example, the signal processor 104 builds aninitial velocity model of the target area 101, acquires seismic datafrom the target area 101, and then iteratively updates the initialvelocity model using the seismic data, obtaining a velocity model closeto the actual seismic velocity distribution of the target area 101.

FIG. 2 is a view for explaining an example of a waveform inversiontheory.

Referring to FIG. 2, a target area 201 has a certain characteristic V.The characteristic V may be one of various characteristics, such as avelocity of a seismic wave, a density or a temperature, for each innerpart of the target area 201. In this case, when a certain input s isapplied to the target area 201, an output d may be observed depending onthe characteristic V. That is, the output d depends on the input s andthe characteristic V. For example, under the same input s, a change ofthe characteristic V of the target area 201 may change the output d.Since the subsurface of the target area 201 can be easily modeled byobtaining the seismic velocity distribution with respect to the targetarea 201 among various characteristics of the target area 201, in thecurrent example, it may be presumed that the characteristic V is aseismic velocity with respect to each inner part of the target area 201.

In this case, the target area 201 may be modeled using a velocityparameter m. Since the velocity parameter m will be iteratively updatedlater, at an initial stage, all inner parts of the target area 201 maybe assigned the same velocity parameter. After the velocity parameter mis set, an output u when a certain virtual input s is applied to amodeled target area 202 may be obtained. That is, the output ucorresponds to the output d, and if the velocity parameter m has beenset to the same as the actual characteristic V, the output u may beequal to the output d. In other words, by adjusting the velocityparameter m such that the output u is equal to the output d, the samevelocity parameter m as the actual characteristic V may be obtained.

Through such waveform inversion, the subsurface imaging apparatus mayacquire measured data d and modeled data u for a target area, adjust thevelocity parameter m such that the difference between the measured datad and modeled data u is minimized to estimate the characteristic V forthe target area, and then create a velocity model and image data for thetarget area using the velocity parameter m (or the characteristic V).

FIG. 3 is a diagram illustrating an example of a subsurface imagingapparatus 300. The subsurface imaging apparatus 300 may correspond to apart of the signal processor 104 illustrated in FIG. 1.

Referring to FIG. 3, the subsurface imaging apparatus 300 may include anobserved wavefield acquiring unit 301, a parameter storage 302, amodeled wavefield creator 303, an energy calculator 304, a parameterupdating unit 305, and a velocity model creator 306.

The observed wavefield acquiring unit 301 acquires an observed wavefieldfrom a target area. The observed wavefield may be seismic data measuredfrom the target area. In the current example, the observed wavefield isrepresented as d.

The parameter storage 302 may store characteristic parameters for thetarget area. For example, the parameter storage 302 may store velocityparameters that represent the seismic velocities with respect toindividual inner parts of the target area. The initial values of thecharacteristic parameters, which are stored in the parameter storage302, may be set by a user and updated later by the parameter updatingunit 305. In the current example, velocity parameters that are stored inthe parameter storage 302 and updated by the parameter updating unit 305are represented as m.

The modeled wavefield creator 303 creates a modeled wavefieldcorresponding to the observed wavefield using the characteristicparameters stored in the parameter storage 302. In the current example,the modeled wavefield is represented as u. A method of creating amodeled wavefield may be described in more detail, below.

When Fourier transform is performed on a wave equation in a time domainfor a certain target area, a wave equation in a frequency domain isdeduced below.

Ku(ω)+iωCu(ω)−ω² Mu(ω)=f(ω)  (1)

In Equation (1), w represents an angular frequency, u(ω) represents adiscrete wavefield, M represents a mass matrix, C represents a viscousdamping matrix, K represents a stiffness matrix, and f(ω) represents atransmission waveform in a frequency domain.

Equation (1) can be rewritten for simplicity, below.

Su=f

S=K+iωC−ω ² M  (2)

In Equation (2), S represents a complex impedance matrix and reflects acharacteristic parameter (for example, a velocity parameter) for atarget area. In other words, the modeled wavefield creator 303 mayobtain a complex impedance matrix S using a velocity parameter M storedin the parameter storage 302, and define a modeled wavefield u based onthe complex impedance matrix S and the transmission waveform f.

After the observed wavefield d and the modeled wavefield u are obtained,the energy calculator 304 calculates accumulated energy which is definedas energy accumulated over time with respect to the observed wavefield dand the modeled wavefield u in the time domain. For example, the energycalculator 304 may calculate accumulated energy by integrating the p-thpower of the absolute value of each of the observed wavefield d andmodeled wavefield u over time. For example, the accumulated energy ũ^(p)of the modeled wavefield u can be calculated as follows.

ũ ^(p)(τ_(min),τ_(max))=∫_(τ) _(min) ^(τ) ^(max) |u(t)|^(p) dt(0≦τ_(min)<τ_(max) ≦t _(max))  (3)

According to Equation (3), the accumulated energy ũ^(p) of the modeledwavefield u is obtained by taking the absolute value of the modeledwavefield u and integrating the p-th power of the absolute value fromτ_(min) to τ_(max). The integration interval may be represented as atime-window applied to the observed wavefield and the modeled wavefield.In the current example, the size of the time window is from τ_(min) toτ_(max), however, may be set to any other interval.

In this way, by the energy calculator 304 converting the observedwavefield d and the modeled wavefield u into energy, waveform inversionusing low frequency components is possible so that a more accuratevelocity model and image data can be obtained. For example, referring toFIGS. 6A and 6B, FIG. 6A shows an observed wavefield and FIG. 6B showsenergy of the observed wavefield. As seen as data from 0 to 2 seconds,in FIG. 6A, there are little low frequency components below 5 Hz,whereas in FIG. 6B showing data converted into energy, there are manylow frequency components below 5 Hz.

Referring again to FIG. 3, after the accumulated energy {tilde over(d)}^(p) of the observed wavefield d and the accumulated energy ũ^(p) ofthe modeled wavefield u are calculated, the parameter updating unit 305updates the characteristics parameter stored in the parameter storage302 such that the difference between the accumulated energy {tilde over(d)}^(p) of the observed wavefield d and the accumulated energy ũ^(p)the modeled wavefield u is minimized. For example, the parameterupdating unit 305 may define an objective function that represents thedifference between the accumulated energy {tilde over (d)}^(p) of theobserved wavefield d and the accumulated energy ũ^(p) of the modeledwavefield u, and update the characteristic parameter stored in theparameter storage 302 using the gradient of the objective function.According to an example, the objective function may be defined using theaccumulated energy {tilde over (d)}^(p) of the observed wavefield d andthe accumulated energy ũ^(p) of the modeled wavefield u. In order toexpress the objective function as an equation, the accumulated energies{tilde over (d)}^(p) and ũ^(p) are subject to Fourier Transform andrewritten to:

ũ ^(p)(m,τ ₀,τ,ω)=∫_(τ) ₀ ^(τ) |u(m,t)|^(p) e ^(−iατ) dt (0≦τ₀ <τ≦t_(max))  (4)

In Equation (4), m represents the characteristic parameter and t_(max)represents the maximum recording time. Then, time integration isperformed on the initial and zero frequency components of the observedwavefield d, and Equation (4) can be rewritten to:

ũ ₀ ^(p)(m,τ)=ũ ^(p)(m,0,τ,0)=∫₀ ^(τ) |u(m,t)|^(p) dt  (5)

Referring to Equations (3), (4), and (5), the accumulated energy ũ^(p)of the modeled wavefield u is equal to the zero frequency component ofthe p-th power of the absolute value of the modeled wavefield u.Meanwhile, in order to minimize the difference between the accumulatedenergy {tilde over (d)}^(p) of the observed wavefield d and theaccumulated energy ũ^(p) of the modeled wavefield, the objectivefunction may be defined, below.

$\begin{matrix}{\begin{matrix}{E_{j} = {\sum\limits_{s,r}\; {\frac{1}{2}{\int_{0}^{t_{j}}{( {{{\overset{\sim}{u}}_{0}^{p}( {m,\tau} )} - {{\overset{\sim}{d}}_{0}^{p}(\tau)}} )^{2}\ {\tau}}}}}} \\{{= {\sum\limits_{s,r}\; {\frac{1}{2}{\int_{0}^{t_{j}}{( {{\int_{0}^{\tau}{{{u( {m,t} )}}^{p}\ {t}}} - {\int_{0}^{\tau}{{{d(t)}}^{p}{t}}}} )^{2}{\tau}}}}}},}\end{matrix}{{j = 1},\ldots \mspace{14mu},n,{0 \leq t_{j} \leq \tau}}} & (6)\end{matrix}$

In Equation (6), j represents a sample of each zero frequency component,and each sample may be obtained by adjusting the size of a time-windowor the r value. In Equation (6), the characteristic parameter m can beupdated in the direction in which the objective function is reduced,below.

$\begin{matrix}{{m^{l + 1} = {m^{l} - {( {H_{a} + {\lambda \; I}} )^{- 1}{\nabla_{m}E}}}}{where}{{H_{a} = {J^{T}J}},{J = \lbrack {\frac{\partial{\overset{\sim}{u}}_{0}^{p}}{\partial m_{1}}\mspace{14mu} \frac{\partial{\overset{\sim}{u}}_{0}^{p}}{\partial m_{2}}\mspace{14mu} \cdots \mspace{14mu} \frac{\partial{\overset{\sim}{u}}_{0}^{p}}{\partial m_{M}}} \rbrack}}} & (7)\end{matrix}$

In Equation (7), m^(l+1) represents an updated characteristic parameter,H_(a) represents the approximated Hessian, J represents the Jacobian, λIrepresents the damping coefficient, and ∇_(m)E represents the gradientof the objective function. In Equation (7), the gradient of theobjective function can be calculated from the steepest descentdirection, by the following Equation.

$\begin{matrix}{{\frac{\partial E_{j}}{\partial m_{k}} = {\sum\limits_{s,r}\; {\int_{0}^{t_{j}}{( {{{\overset{\sim}{u}}_{0}^{p}( {m,\tau} )} - {{\overset{\sim}{d}}_{0}^{p}( {m,\tau} )}} )\ \frac{\partial{{\overset{\sim}{u}}_{0}^{p}( {m,\tau} )}}{\partial m_{k}}{\tau}}}}},{j = 1},\ldots \mspace{14mu},n} & (8)\end{matrix}$

Also, in Equation (8), the partial derivative value of the accumulatedenergy ũ^(p) of the modeled wavefield u with respect to thecharacteristic parameter m can be calculated by numerical approximationaccording to the finite differential method and the Taylor expansion, asfollows in Equation (9):

$\begin{matrix}{\frac{\partial{{\overset{\sim}{u}}_{0}^{p}( {m,\tau} )}}{\partial m_{k}} = {{\frac{\partial}{\partial m_{k}}{\int_{0}^{\tau}{{{u( {m,t} )}}^{p}{t}}}} \approx \frac{{\int_{0}^{\tau}{{{u( {{m + {\Delta \; m_{k}}},t} )}}^{p}\ {t}}} - {\int_{0}^{\tau}{{{u( {m,t} )}}^{p}\ {t}}}}{\Delta \; m_{k}} \approx \frac{{\int_{0}^{\tau}{{{{u( {m,t} )} + {\Delta \; m_{k}\frac{\partial{u( {m,t} )}}{\partial m_{k}}}}}^{p}\ {t}}} - {\int_{0}^{\tau}{{{u( {m,t} )}}^{p}\ {t}}}}{\Delta \; m_{k}}}} & (9)\end{matrix}$

Referring to FIG. 3, after the parameter updating unit 305 updates thecharacteristic parameter m using Equations (4) to (9), the updatedcharacteristic parameter is stored in the parameter storage 302, and themodeled wavefield creator 303 performs modeling using the updatedcharacteristic parameter. The process may be repeated until theobjective function becomes smaller than a predetermined threshold value.

Meanwhile, according to another example, the objective function may bedefined using a value obtained by taking the logs of the accumulatedenergy ũ^(p) of the observed wavefield d and the accumulated energyũ^(p) of the modeled wavefield. For example, the objective function maybe defined as Equation (10) below.

$\begin{matrix}{{E_{j} = {\sum\limits_{s,r}\; {\frac{1}{2}{\int_{0}^{t_{j}}{( {\log ( \frac{{\overset{\sim}{u}}_{0}^{p}( {m,\tau} )}{{\overset{\sim}{d}}_{0}^{p}(\tau)} )} )^{2}\ {\tau}}}}}},{j = 1},\ldots \mspace{14mu},n} & (10)\end{matrix}$

Also, when the objective function is defined using the log, the steepestdescent direction for updating the characteristic parameter m can begiven as Equation (11):

$\begin{matrix}{{{\frac{\partial E_{j}}{\partial m_{k}} = {\sum\limits_{s,r}\; {\int_{0}^{t_{j}}{{\log ( \frac{{\overset{\sim}{u}}_{0}^{p}( {m,\tau} )}{{\overset{\sim}{d}}_{0}^{p}(\tau)} )}\frac{1}{{\overset{\sim}{u}}_{0}^{p}( {m,\tau} )}\ \frac{\partial{{\overset{\sim}{u}}_{0}^{p}( {m,\tau} )}}{\partial m_{k}}{\tau}}}}},{j = 1},\ldots \mspace{14mu},n}{{where}\mspace{14mu} {the}\mspace{14mu} {Jacobian}\mspace{14mu} {is}\mspace{14mu} \frac{1}{{\overset{\sim}{u}}_{0}^{p}( {m,\tau} )}\frac{\partial{{\overset{\sim}{u}}_{0}^{p}( {m,\tau} )}}{\partial m_{k}}}} & (11)\end{matrix}$

Referring again to FIG. 3, the characteristic parameter m is iterativelyupdated until the objective function becomes smaller than thepredetermined threshold value, and the velocity model creator 306creates a velocity model for the target area using the finally updatedcharacteristic parameter. The velocity model created by the velocitymodel creator 306 may be an initial velocity model for creating imagedata. As described above, since the modeling and objective functionaccording to the current example is based on accumulated energy and lowfrequency components, a more accurate image for the subsurface can beobtained by creating image data for the subsurface using theinitial-velocity model.

FIG. 4 is a flowchart illustrating an example of a subsurface imagingmethod.

The subsurface imaging method will be described with reference to FIGS.1, 3 and 4, below.

First, an observed wavefield for a target area is acquired (401). Forexample, the observed wavefield acquiring unit 301 receives seismic datathrough the plurality of receivers 103 provided on the target area 10,thus acquiring an observed wavefield d.

Then, a characteristic parameter for the target area is established(402). For example, an initial value of a velocity parameter may bestored as a characteristic parameter in the parameter storage 302.

Then, a modeled wavefield u corresponding to the observed wavefield d iscreated using the characteristic parameter (403). For example, themodeled wavefield creator 303 may create a modeled wavefield u usingEquations (1) and (2).

Then, accumulated energies for the observed wavefield d and modeledwavefield u are calculated (404). For example, the energy calculator 304may calculate the accumulated energy {tilde over (d)}^(p) of theobserved wavefield d and the accumulated energy ũ^(p) of the modeledwavefield u using Equations (1) and (2).

Then, the characteristic parameter is updated, such that the differencebetween the accumulated energy ũ^(p) of the observed wavefield d and theaccumulated energy ũ^(p) of the to modeled wavefield u is minimized(405). For example, the parameter updating unit 305 may update thecharacteristic parameter using Equations (4) to (11).

After the characteristic parameter is updated, a velocity model for thetarget area is created using the updated characteristic parameter (406).For example, the velocity model creator 306 may create a velocity modelfor the target area using a parameter stored in the parameter storage302.

FIG. 5 is a flowchart illustrating an example of a characteristicparameter updating method.

Referring to FIG. 5, in order to update the characteristic parametersuch that the difference between the accumulated energy ũ^(p) of theobserved wavefield d and the accumulated energy ũ^(p) of the modeledwavefield u is reduced, an objective function is defined using each ofthe accumulated energies {tilde over (d)}^(p) and ũ^(p) (501). Forexample, the parameter updating unit 305 may define the objectivefunction using Equation (6) or (10).

After the objective function is defined, it is determined whether theobjective function or the difference between the accumulated energies{tilde over (d)}^(p) and ũ^(p) is below a predetermined threshold value(502). If the objective function is not within a predetermined thresholdrange, the gradient of the objective function is calculated in order toupdate the characteristic parameter in the direction in which theobjective function is reduced (503). For example, the parameter updatingunit 305 may calculate the gradient of the objective function usingEquations (8), (9), and (11), and update the characteristic parameterusing the gradient of the objective function (504). For example, theparameter updating unit 305 may update the characteristic parameterusing Equation (7).

Then, a modeled wavefield u is recreated using the updatedcharacteristic parameter (505) and the process is repeated until theobjective function is within the predetermined threshold range.Thereafter, when the objective function becomes smaller than apredetermined threshold value, a velocity model is created using thefinally updated characteristic parameter (506).

As described above, according to the subsurface imaging apparatus andmethod, since waveform inversion is performed after a wavefield isconverted into energy accumulated over time, low frequency componentsmay be efficiently used-so that a more accurate image for the subsurfacecan be acquired.

The processes, functions, methods and/or software described above may berecorded, stored, or fixed in one or more computer-readable storagemedia that includes program instructions to be implemented by a computerto cause a processor to execute or perform the program instructions. Themedia may also include, alone or in combination with the programinstructions, data files, data structures, and the like. The media andprogram instructions may be those specially designed and constructed, orthey may be of the kind well-known and available to those having skillin the computer software arts. Examples of computer-readable mediainclude magnetic media, such as hard disks, floppy disks, and magnetictape; optical media such as CD-ROM disks and DVDs; magneto-opticalmedia, such as optical disks; and hardware devices that are speciallyconfigured to store and perform program instructions, such as read-onlymemory (ROM), random access memory (RAM), flash memory, and the like.Examples of program instructions include machine code, such as producedby a compiler, and files containing higher level code that may beexecuted by the computer using an interpreter. The described hardwaredevices may be configured to act as one or more software modules inorder to perform the operations and methods described above, or viceversa. In addition, a computer-readable storage medium may bedistributed among computer systems connected through a network andcomputer-readable codes or program instructions may be stored andexecuted in a decentralized manner.

A number of examples have been described above. Nevertheless, it will beunderstood that various modifications may be made. For example, suitableresults may be achieved if the described techniques are performed in adifferent order and/or if components in a described system,architecture, device, or circuit are combined in a different mannerand/or replaced or supplemented by other components or theirequivalents. Accordingly, other implementations are within the scope ofthe following claims.

1. An apparatus of imaging a subsurface of a target area, the apparatuscomprising: an observed wavefield acquiring unit configured to acquirean observed wavefield for a target area based on seismic data; aparameter storage configured to store a characteristic parameter for thetarget area; a modeled wavefield creator configured to create a modeledwavefield corresponding to the observed wavefield using thecharacteristic parameter stored in the parameter storage; an energycalculator configured to calculate accumulated energies of the observedwavefield and the modeled wavefield, the accumulated energies beingdefined as energies accumulated over time with respect to the observedwavefield and the modeled wavefield; and a parameter updating unitconfigured to update the characteristic parameter stored in theparameter storage such that a difference between the accumulated energyof the observed wavefield and the accumulated energy of the modeledwavefield is minimized.
 2. The apparatus of claim 1, wherein the energycalculator is further configured to calculate the accumulated energiesof the observed wavefield and the modeled wavefield, based on valuesobtained by integrating the p-th powers of absolute values of theobserved wavefield and the modeled wavefield over time.
 3. The apparatusof claim 1, wherein the parameter updating unit is further configuredto: define an objective function that represents a difference betweenthe accumulated energy of the observed wavefield and the accumulatedenergy of the modeled wavefield at each time-window; and update thecharacteristic parameter using a gradient of the objective function. 4.The apparatus of claim 3, wherein the parameter updating unit is furtherconfigured to define the objective function using the accumulated energyof the observed wavefield and the accumulated energy of the modeledwavefield.
 5. The apparatus of claim 3, wherein the parameter updatingunit is further configured to define the objective function using valuesobtained by taking logs of the accumulated energy of the observedwavefield and the accumulated energy of the modeled wavefield.
 6. Theapparatus of claim 3, wherein the parameter updating unit is furtherconfigured to calculate the gradient of the objective function using aJacobian with respect to a characteristic parameter of the accumulatedenergy of the modeled wavefield.
 7. The apparatus of claim 6, whereinthe parameter updating unit is further configured to calculate theJacobian with respect to the characteristic parameter of the accumulatedenergy of the modeled wavefield, by numerical approximation according toa finite differential method.
 8. The apparatus of claim 1, wherein thecharacteristic parameter comprises a seismic velocity with respect tothe target area.
 9. The apparatus of claim 1, further comprising avelocity model creator configured to create a velocity model of thetarget area using the updated characteristic parameter.
 10. A method ofimaging a subsurface of a target area, the method comprising: acquiringan observed wavefield for a target area based on seismic data; setting acharacteristic parameter for the target area and creating a modeledwavefield corresponding to the observed wavefield using thecharacteristic parameter; calculating accumulated energies of theobserved wavefield and the modeled wavefield, wherein the accumulatedenergies are defined as energies accumulated over time with respect tothe observed wavefield and the modeled wavefield; and updating thecharacteristic parameter such that a difference between the accumulatedenergy of the observed wavefield and the accumulated energy of themodeled wavefield is minimized.
 11. The method of claim 10, wherein thecalculating of the accumulated energies of the observed wavefield andthe modeled wavefield comprises calculating the accumulated energies ofthe observed wavefield and the modeled wavefield, based on valuesobtained by integrating the p-th powers of absolute values of theobserved wavefield and the modeled wavefield over time.
 12. The methodof claim 10, wherein the updating of the characteristic parametercomprises: defining an objective function that represents a differencebetween the accumulated energy of the observed wavefield and theaccumulated energy of the modeled wavefield at each time-window; andupdating the characteristic function using a gradient of the objectivefunction.
 13. The method of claim 12, wherein the updating of thecharacteristic parameter comprises defining the objective function usingthe accumulated energy of the observed wavefield and the accumulatedenergy of the modeled wavefield.
 14. The method of claim 12, wherein theupdating of the characteristic parameter comprises defining theobjective function using values obtained by taking logs of theaccumulated energy of the observed wavefield and the accumulated energyof the modeled wavefield.
 15. The method of claim 12, wherein theupdating of the characteristic parameter comprises calculating thegradient of the objective function using a Jacobian with respect to acharacteristic parameter of the accumulated energy of the modeledwavefield.
 16. The method of claim 15, wherein the updating of thecharacteristic parameter comprises calculating the Jacobian with respectto the characteristic parameter of the accumulated energy of the modeledwavefield, by numerical approximation according to a finite differentialmethod.
 17. The method of claim 10, wherein the characteristic parametercomprises a seismic velocity with respect to the target area.
 18. Themethod of claim 10, further comprising a velocity model of the targetarea using the updated characteristic parameter.